To look out means to watch carefully for something, especially danger or something important that might be coming. When a ship's captain stationed a sailor in the crow's nest to look out for land or icebergs, that sailor had one job: pay attention and warn everyone else. When you're riding your bike and a friend yells “Look out!” they're warning you about something you haven't noticed yet, maybe a pothole or a car backing up.

The phrase suggests active watching, not just casual glancing around. A crossing guard looks out for children crossing the street. A weather forecaster looks out for signs of dangerous storms. Parents look out for their children's safety and well-being.

A lookout (one word) is either a person whose job is watching for danger, or a high place used for watching. A lifeguard at a beach sits in a lookout tower to look out for swimmers in trouble.

The phrase can also mean to take care of someone. When you promise to look out for your younger cousin at recess, you're saying you'll make sure they're okay and help if they need it. That's why “look out for yourself” means take care of yourself, while “look out for each other” means help protect one another.